How to Calculate a Two Way ANOVA (factorial analysis)

[@MetropolitanChic]

7 years later, and your still helping me in 2020. Passing my final exam now.

[@mj2625]

Felt in 2021

[@statisticsfun]

Thanks! I use a variety of different software including photoshop, illustrator, HTML5, Final Cut, GarageBand and a few other products. Each video takes me a long time to create. My rule of thumb is each minute of video takes about 12 hours to create, so a 7 minute video takes me about 84 hours of development time. Good luck on your presentation.

[@redkarryn]

and yet, priceless when it comes to value!

[@carlosaldana6039]

Can I use two way anova in solving 3 factor experiments?

[@socratesoliveira1176]

Thank you so much, man!

[@sylviaemejuru1956]

Woow! Thank you again!

[@aurorasart9458]

Thank you for you very nice job!!!

[@Persplained]

Still useful 10 years later. Best use of video to explain a topic in a lecture style way, no useless animation but perfectly understandable. That must take a lot of work. Thank you for making these video's. Best video's on youtube for stats

[@abnormia]

I watched 2 x 2 hour lectures from my uni about factorial analysis and had no idea wtf he was talking about. I watch this youtube video which is 18 minutes and understand it... you are a life saver! Thank you!

[@stavanmehta1285]

one of the only few genuinely decent and complete explanations of two-factor ANOVA

[@statisticsfun]

You are welcome, welcome, welcome! I really appreciate hearing from students and it does make my day to hear that my videos are helping.

[@afd8507]

Saved Me and my final in 2024, insanely helpful video

[@paulhan3536]

searched the website for couple days to try to figure out how to solve this by hand and EVERYWHERE i looked... people did them by excel or other programs and just wrote out the answers without showing any work... thank you SO much for this video. helped a lot.

[@SilenceDestroier]

You know, channel lives up to it's name, dude made me actually have fun with statistics for the first time in a couple of years. Great channel and explanations are top notch

[@huichen6461]

extremely high quality, very intelligent, and elegant. The speed is great. not slow at all. I can watch it while thinking. I would absolutely ignore any not constructive comments.

[@hasben0]

Really apreciate you for taking the time to make all the graphics, makes the leson easy to digest!

[@statisticsfun]

Thank you very much for your compliments. I believe the 1.3 = 1.8 is a rounding error. I don't carry all the digits through the entire problem.

[@slimahmoud]

Amazing Tutorials!! Many thanks I have only one comment (kind of silly), but the square of 1.3 = 1.69 and not 1.8 Thanks again and they are really very helpful tutorials with great explanation... Regards

[@edsnowden7576]

Same question,

[@IfeanyiUkwuoma]

Greatest Teacher Ever! Am going to tell the Whole World how Statisticsfun made me get an A+ in my Masters Thesis.. Working with Caterpillar Global Mining and I had to apply statistics to determine the variability between coal production and methane emission...with this Video, I looked like a pro :-) Hope to see you someday! You are the Best!!! *So Grateful*

[@statisticsfun]

Awesome!!!!! Thank you for spreading the word and congratulations on your A+. You deserve all the credit.

[@learnwithamber7765]

It's very clear when you break it down. Now I know what my professor was talking about!. Thanks!

[@marisawyman9674]

Currently taking my final and I couldn’t do it without this video 🙏🏼

[@Januaryblues100]

This video series helped me understand these concepts better than my professor did, you just saved my Pysch Stats grade. Thankyou, very easy to listen to and understand.

[@xiaxiading7806]

It is my first comment on KZbin. I can not wait to share it with my friends. It is thousands of help. Thanks for the pretty vision and explanation.

[@sebastianjensch5203]

Advice: Play in x1.25. Great vid!

[@ObhiReads]

Very helpful. There are minor mistakes still such a long process anyway gets benefit of doubt. Thanks for the easy explanation

[@jokertaylor6492]

This is so precious, thank you so much for making these and uploading these. I'm gonna pass my exam.

[@krisghimire6938]

Thanks a Lot! helped me understand Two way ANOVA much better from your video than from my professor. Keep making more !!

[@kyounokaze]

Thank you for making statistics so much simpler to understand. Your videos have helped me and thousands more.

[@carlosp.e.bedson4011]

Such an awesome video. Thank you so much for taking the time to show so simply and transparently how this all works.

[@statisticsfun]

Many thanks for the comment. Make sure you like MyBookSucks on FaceBook (see link in video description). This will help others find the educational videos.

[@jgrtrx]

I like the clean presentation style. Very nice work.

[@christytanner3896]

I was going 2 say you made a mistake on SSe but I see it was just wrong on screen. Thank you for doing it step-by-step bc I've been looking everywhere for someone to break it down 4 me. Math is not my best subject...at all!!

[@summertummer2394]

Marvellous. You are great. The graphical interface you use is excellent.

[@sarah-louisedench3373]

Amazing! Thank you so much. Not only can I do this now but I actually understand the logic behind it, and at a brilliant pace. Thanks! :)

[@statisticsfun]

Sarah-Louise Dench You are very welcome. If you get a chance make sure you like and share the videos, it will make it easy for others to find them.

[@sarahwest4926]

thanks again for clarifying that SSW is "error." Not getting that concept can completely wreck a calculation---writing a good interpretation is impossible without it.

[@ericthehalfabee1]

Thanks very much, sir. Most illuminating indeed! Deeply appreciate your taking the time to help out folks like me, who have been struggling with this.

[@statisticsfun]

Eric Smith Eric, I always appreciate hearing my videos are helpful. I spend a tremendous amount of time on them (about 8 hours for every minute of video). Hopefully you will like, share, subscribe, If you get a chance could you please like our FB page. www.FaceBook.Com/PartyMoreStudyLess It will help others find the videos.

[@brendapoole8490]

I enjoyed watching the video on the two-way ANOVA design. I finally learned how to compute the measured to interpret the data. Also, a big thank you for demonstrating such great examples. Thank you!

[@CMAuProductions]

I cannot express my thanks enough. These videos are great!

[@balayet03]

You have helped get me one step closer to maybe passing my exam! Thank you!!

[@shn1804]

Thank you so much for this-Its hard to find such a clear presentation on doing two way ANOVA's by hand

[@emmaobrien7431]

Thank you! Great video. Why did you use the averages of each age group from which you subtracting the grand mean instead of using the row means to calculate SS age?

[@statisticsfun]

Jenn, nice to hear my videos are helping you towards your PhD. Btw, what is the subject are of your PhD?

[@statisticsfun]

Good catch. I hope (I don't think) it makes a difference, but I will correct that when I revise the video. Thanks again for the catch, you have an eve for detail.

[@michaeljoppa2155]

at 12:49 in the video you show that the boys score of 6-7= (-2.0)2 Wouldn't it be (-1)2? Plus isn't the sum of squares equal to 31?

[@JasTheKariol]

28 is the correct sum of squares if the correct value is considered for (6-7)² = 1 instead of 4.

[@ileanaquintero5002]

Thank you so much! I have an exam this week and my teacher goes through things super fast and textbooks just don't do it for me.

[@statisticsfun]

Appreciate that! Always good to know my videos are helping. Make sure you like MyBookSucks on FaceBook (see link in video description). This will help others find the educational videos.

[@bogdandobondi8128]

Awesome! Purely awesome. You put the fun back into statistics - the fun that got sucked out by the book of John A. Rice. With all due respect to him.

[@statisticsfun]

As always you are very welcome and good luck this week too.

[@wandaparsons8331]

Thank-you for your time putting this together, very helpful!

[@statisticsfun]

I checked! Holy Cow Batman. You have great ears and eyes and a keen perspective on detail. You are correct.

[@divyatopwal3190]

Sir will u help me out to how to analyse the data for crd design if the data is based on germination test done in lab.

[@bhakthirai8166]

how did u get the square of -1.3 to be 1.8? even if u round figure it, it must be 1.7

[@Kevin2341]

Oh, and thank you very much for the videos, you explain it very clearly!

[@odalovesjustin]

Amazing videos! I´m so glad i found these. Thank you for taking so much time in making these :D

[@clockwork4068]

It's actually mindblowing how most of your audience rely on memorization of 'lo-and-behold' facts and consider themselves to be learning the subject

[@sheilaachieng809]

Show us your ways then 🥴

[@IR240474]

Thank you!! This was really cool and well explained - going for part 3 then to bed, Two-Way ANOVA at 10am

[@kirbyy]

thejamesbond, i wondered the same thing. I calculated the ss for the second factor according to "test scores" and it did give the same result as the method in the video.

[@user-xn2hf9re8r]

put simply, thank God you exist

[@sergioc2989]

Thank you!!! so much!!! you can't understand how much this video help me!! really! thank you!

[@hilalozkececi1900]

thanks a lot for the effort, statistics isn't a nightmare anymore!

[@statisticsfun]

Hilal özkeçeci Glad that you are no longer having statistics nightmare, best to keep your dreams to happy dreams. Hopefully you will like, share, subscribe, If you get a chance could you please like our FB page. www.FaceBook.Com/PartyMoreStudyLess It will help others find the videos.

[@andreib8871]

Thank you for video! When you calculate Sum of squares for Gender you do this separetly for boys and girls. I expected that for second factor age it would be separate calculation for each category 10YO, 11YO, 12YO. Could you please clarify why it is used different approach for caluculation sum of squares for factor 1 and factor 2?

[@shobhitverma3290]

I had the same question. Although the final answer is correct, calculating means based on Age would have been more intuitive.

[@ultinatetruustar]

It does seem much easier than I expected. Great videos.

[@kirbyy]

thanks so much for these videos!! im doing complex analysis for my thesis and these help me a lot in understanding the reasoning behind it all. though its too bad you didnt show how to calculate the interaction by hand i am curious about that too.

[@yasser19781]

This vedio helped me alot in analyzing my data for my project , many thanks

[@robbieklein6162]

For main effects, it would be clearer if the whole thing were framed in terms of a ratio between between groups/factor variance and within-group variance. But for the age factor, you organize the data by gender. This makes the overall functioning of the f-ratio for the age effect unclear for beginners

[@saebelorn]

I think it may have helped to have mention or emphasise that the within-group variance is calculated for each 'group', 'treatment', however you call it, rather than combining the factors together completely

[@statisticsfun]

Many thanks! Make sure you like MyBookSucks on FaceBook (see link in video description). This will help others find the educational videos.

[@statisticsfun]

Thank you for you compliments. It is much appreciated. Make sure you like MyBookSucks on FaceBook (see link in video description). This will help others find the educational videos.

[@statisticsfun]

Thanks for that. I will double check the video. I appreciate the help.

[@slimahmoud]

Yes I have noticed that also at the end of the video with the same rounding being made by the software... Thank you again :)

[@statisticsfun]

I believe that is a rounding error. Keep in mind that in all of statistics we are estimating, so rounding should not make a lot of difference. It is hard to carry more than one decimal when you are doing calculations by hand.

[@pedantsunited5368]

you're a lifesaver

[@PatrickQ]

Excellent! Very nice presentation, and very clear. Thank you for taking the time to put this together. I don't suppose you might do a video on the estimation of parameters in linear regression models?

[@speedyraptor9]

Please give an example of three-way ANOVA, if you do not mind. Your videos are great!

[@hetvimodi6137]

You are so patient with the entire process. Thank you for explaining this topic so well. So do I get an award by mail or what? :D Thanks once again.

[@coldpineapples9328]

great vid!! very comprehensive and easy to understand!!

[@mandelanwa7472]

am so happy to watch this.... I really enjoy it Thanks allot # PROUDLY A STATISTICIAN #

[@eesa6463]

Thank you God bless you sir.

[@hannahwilliams9983]

Is this a type 1, 2 or 3 sum of squares? I know it doesn't matter because it's balanced but I am curious?

[@jenssoet8382]

@statisticsfun maybe a dumb question, but can I calculate the SST as well if I don’t have any individual test scores but only group means? Thanks a lot for the video btw

[@bxatch]

this is so calming

[@susanarios7825]

Very helpful. I have to present a two-way ANOVA to others in the class next week and had no clue how to... now I do. Thanks! Also, what computer program did you use to put the presentation where you can move the data, highlight them, etc.?

[@alexandraxanthopoulou6853]

you just saved my day my friend

[@allivecars]

thankyou u save my life

[@jamenlong1097]

At about 7:17, you calculate the first component of the first factor sum of squares. You do this by repeating nine times, the boys average (7.7) minus the grand mean (9) and squaring the result, (7.7-9)^2, then summing all of this to get 16 as the boys sum of squares. It seems that you could get a more granular and accurate measure of the sum of squares if you subtracted the grand mean (9) from the individual scores. Why is this not done? I realize that it would increase the sum of squares and affect the F tests later on, but it seems more accurate. Why is it that using the boys mean in place of each score is acceptable when it seems less accurate?

[@user-hongkongnews]

I think they are two different things. One is called sum of squares between the group, one is called sum of squares within the group. So basically our goal is to see whether different group are the same. So we compare differences between group mean and ground mean, and differences within the group. If they are very different, we reject hypothesis. Think about this way. You probably have three class , which all have average 81 points, 82 points and 83 points. If you calculate average of (81+81+82) to get your group mean, then the differences between each group mean and your ground mean would be very small. However, it is possible that most of students in group one are around 81, while in group two there are some students get 90, while some get 72, which also give average 81. However, obviously these two groups will be very different even if they have same average.Then you calculate differences between each data point in a group and the mean of the group it is in.(called sum of square within) Then, you compare sum of square between and sum of square within. If the ratio is very large, that means your different group perform very different even if they have similar mean

[@senthilcaesar]

Thank you so much for this lecture...

[@arnolddelacruz7822]

Awesome video with clear and easy to follow explanation. By the way, is this with or without replication? thanks

[@statisticsfun]

Appreciate that! Make sure you like MyBookSucks on FaceBook (see link in video description). This will help others find the educational videos.

[@sylviaemejuru1956]

Thank you very much Sir! I am so grateful!

[@a.chikkuchimathematics7386]

Thank you so much for making it so simple.

[@younessaitoummou7934]

Thank you very much, this video is really useful !

[@paranjaygulati9661]

hi great videos , in 7:13 (-1.3)^2 is 1.7 not 1.8, pls note this calculation error everyone who's watching

[@Juriaan93]

Very well explained

[@statisticsfun]

Good luck on your exam!!!!! Make sure you like MyBookSucks on FaceBook (see link in video description). This will help others find the educational videos.

[@statisticsfun]

I do have an example of doing Two Way Analysis by hand. I have an entire playlist on Two ANOVA. You can find the link to the playlist in this videos description. The first video in the playlist shows how to calculate Two ANOVA by hand. Good luck on your thesis as well. Btw, What is your topic of your thesis?

[@duongquyhuynh4294]

Hi, I have trouble with the Sum of Squares Total. I used SPSS to calculate, SSFactor1, SSFactor2 and the SSWithin are correct. But the SSTotal is not Its have 2 values: "Total" and "Corrected total". The "Corrected Total" is the same values as you calculated here, but the "Total" one, what is it and how can i calculate it? I used the tool "Univariate..." in Analyze> General Linear Model. Many thanks!

[@kevinchyung2026]

Thank you for this. This was incredible

[@rehansiddique7291]

When we take the average of a group overall, do we take the average of the averages, or the average of all of the data? For example, if we had a differing number of observations for each factor, Im not sure if the average of averages would work

[@paug.2665]

So Easy to learn using this video. like like!!

[@statisticsfun]

Pauline Gustilo Thanks for that! Good luck in your studies too.

[@woRstbB]

Hi, can I have more than two independent variables for 2-way Anova :)?

[@statisticsfun]

You are very welcome! Make sure you like MyBookSucks on FaceBook (see link in video description). This will help others find the educational videos.

[@rameshbhaifaldu6636]

VERY NICE FOR THE STUDY, THANK YOU

[@hanslofgren8199]

Hi there, thank you for a very nice layout. I wonder about 11:00 min in the video, where you have the BOYS mean instead of Girls mean (7 green, 10 Brown, 14 Purple) substracted from the grand mean. I thought that the sum of Squares of the Girls should be 90, and the Sum of Squares of the second factor (age) should be 136,5. That leads to a negative Sum of Squares in both factors of -36,5. Am I right or have I misunderstood something?

[@xinihu7273]

Hi many thanks for the video. I would like to ask how could I analyse one independent variable with two different levels’ influence on one dependent variable. For example, how do high level of organisational support and low level of organisational support affect on employee satisfaction? Could you please suggest how to do this? And how to classify the organisational support into high and low level of this collect via seven likert scale. I am confused about using multi group analysis and ANOVA. Many thanks for your help

[@_instanze_]

I really love your videos but it would be nice if you would also include the null hypothesis too as that is usually most of points

[@eniola988]

SO helpful..

[@statisticsfun]

Linda Adeyemo Great to hear and good luck in your studies too.